On the Fundamental Group of the Space of Cubic Surfaces.
On the fundamental groups of some open rational surfaces.
On the homotopy of the complement to plane algebraic curves.
On the irreducible components of characteristic varieties.
On the mixed Hodge structure associated to of a simply connected complex projective manifold
On the Ramification of Branched Coverings of IPn.
On the representations of the fundamental group
On the S-fundamental group scheme
We introduce a new fundamental group scheme for varieties defined over an algebraically closed (or just perfect) field of positive characteristic and we use it to study generalization of C. Simpson’s results to positive characteristic. We also study the properties of this group and we prove Lefschetz type theorems.
On three types of simplicial objects
Parabolic sheaves on higher dimensional varieties.
Prime to fundamental groups and tame Galois actions
We show that for a local, discretely valued field , with residue characteristic , and a variety over , the map to the outer automorphisms of the prime to geometric étale fundamental group of maps the wild inertia onto a finite image. We show that under favourable conditions depends only on the reduction of modulo a power of the maximal ideal of . The proofs make use of the theory of logarithmic schemes.
Profinite homotopy theory.
Projective varieties with non-residually finite fundamental group
Projectivity of Kähler manifolds – Kodaira’s problem
Every compact Kähler surface is deformation equivalent to a projective surface. In particular, topologically Kähler surfaces and projective surfaces cannot be distinguished. Kodaira had asked whether this continues to hold in higher dimensions. We explain the construction of a series of counter-examples due to C. Voisin, which yields compact Kähler manifolds of dimension at least four whose rational homotopy type is not realized by any projective manifold.
Realization of homotopy classes by algebraic mappings.
Relative homotopical depth and a conjecture of Deligne.
Relèvement de schémas et algèbres de Monsky-Washnitzer : théorèmes d’équivalence et de pleine fidélité
Representations of the fundamental group and vector bundles.
Résidus en géométrie algébrique
Revêtements de courbes algébriques